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Geometry Lesson 43.notebook
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October 07, 2011
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Warm Up
1. Name all sides and angles of ∆FGH.
2. What is true about angle K and angle L? Why?
3. What does it mean for two segments to be congruent?
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Use properties of congruent triangles.
Prove triangles congruent by using the definition of congruence.
Objectives
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corresponding anglescorresponding sidescongruent polygons
Vocabulary
Geometry Lesson 43.notebook
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Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if and only if their corresponding sides are congruent. Thus triangles that are the same size and shape are congruent.
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Two vertices that are the endpoints of a side are called consecutive vertices.For example, P and Q are consecutive vertices.
Helpful Hint
P
Q
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To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS. In a congruence statement, the order of the vertices indicates the corresponding parts.
Geometry Lesson 43.notebook
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When you write a statement such as ∆ABC ≅ ∆DEF, you are also stating which parts are congruent.
Helpful Hint
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Example 1: Naming Congruent Corresponding Parts
Given: ∆PQR ≅ STWIdentify all pairs of corresponding congruent parts.
Geometry Lesson 43.notebook
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If polygon LMNP ≅ polygon EFGH, identify all pairs of corresponding congruent parts.
Check It Out! Example 1
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Example 2A: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC ≅ DBC. Find the value of x.
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Given: ∆ABC ≅ DEF
Check It Out! Example 2a
Find the value of x.
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Example 3: Proving Triangles CongruentGiven: ∠YWX and ∠YWZ are right angles. YW bisects ∠XYZ. W is the midpoint of XZ. XY @ YZ. Prove: ∆XYW @ ∆ZYW
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Check It Out! Example 3
Given: AD bisects BE. BE bisects AD. AB ≅ DE, ∠A ≅ ÐD Prove: ∆ABC ≅ DEC
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Geometry Lesson 43.notebook
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